Differential Equation Analysis

2016 ◽  
pp. 113-130
Keyword(s):  
Differential Equation ◽  
Equation Analysis

Towards of Quantitative Model of Stacked Actor-Network Dynamics

2017 ◽  
Vol 9 (2) ◽  
pp. 42-62
Author(s):  
Peter Kopanov ◽  
Ivan Tchalakov
Keyword(s):  
Social Sciences ◽  
Differential Equation ◽  
Quantitative Description ◽  
Quantitative Model ◽  
Cultural Dynamics ◽  
Stable States ◽  
The Third ◽  
Equation Analysis ◽  
Actor Networks ◽  
Technology Growth

This article further develops the stacked actor-networks (SAN) approach in modelling socio-economic and cultural dynamics. Following the Lee and Schiesser application of differential equation analysis in biological and social sciences, the authors used a basic SAN model. This model is composed of three subnetworks where each two subnetworks dominate over the third one to build a quantitative description that identifies three stable states in the dynamics of their interactions – cyclical development, linear, and exponential growth. Describing the latter, the notion of ‘technology growth' is introduced that bears on the pattern of hyper-fast growth.

Dynamic Stresses in a Driven Pile During Installation-Classical Wave Equation Model Solution Using Partial Differential Equations

2014 ◽  
Author(s):  
Syed Muhammad Mohsin Jafri ◽  
Phayak Takkabutr
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Equation ◽  
Closed Form Solution ◽  
Equation Of Motion ◽  
Form Solution ◽  
Design Parameters ◽  
Partial Differential ◽  
Equation Analysis ◽  
Driven Pile

This paper derives and solves the governing dynamic wave equation of motion of a driven pile during the installation phase, when the driven pile is subjected to hammer blows. The pile is assumed as an elastic solid body. The equation of motion is a partial differential equation in space (axial coordinate) and time. The governing partial differential equation of motion is solved for installation boundary conditions, and simplified soil resistance models. The solution of the governing equation yields important design parameters, such as stress variation at any cross-section along the pile length with respect to time, and propagating wave speed. The resulting closed-form solution can be easily implemented using a standard spreadsheet or an engineering calculation program. This approach is compared with conventional wave equation analysis (WEAP) used in industry practice. The conventional wave equation analysis is based on discretization of the pile into mass-spring-damper elements (lumped parameter approach), rather than continuous modeling. The models and solutions from these two approaches are compared.

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